Curve fitting of growing measurement data set

I follow fatigue tests live and record measurement data at defined time intervals. In the end, there is always a curve that can be divided into three areas. See in the picture.

For the various tests, they only differ in terms of the total service life and the gradient in the middle range.

Problem: The complete measurement data can be fitted reasonably well

with a 6th degree polynomial, but this does not work with an incomplete data set.

My question now is: how can I smooth / fit the values ​​during the measurement data acquisition with the boundary condition that a curve of this shape comes out at the end?

Answer 1

[Matt J]

This might help,

https://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling

[Dorothee Boegler]

Thanks! that looks good . I was looking for something like that. Now I have to apply that to my case. But since I'm not that fit with Matlab, it takes a while ... I hope I can manage it that way.

Answer 2

[Mathieu NOE]

hello

this little code snipset in case it fills your needs

% dummy data
n = 200;
x = 1:n;
y = 1-exp(-x/5);
yf = -fliplr(y)+1;
y = y + yf + 0.0025*x + 0.1 * randn(1,n);
figure(1);
plot(x,y);
hold on 

% animated plot simulating data acquisition + smoothing (by polynomial fit)

%// initiallize plot. Get a handle to graphic object

    p1 = plot(0,0,'b',0,0,'dr');
    title('Data Acquisition')
    xlabel('Strain');
    ylabel('Force');
    axis([0 n 0 3]);%// freeze axes to their final size, to prevent Matlab from rescaling them dynamically

    x_acq = []; % init
    y_acq = []; % init
    
for ci = 1:n
    
    % simulate data acquisition and buffer fill
    x_acq = [x_acq x(ci)];
    y_acq = [y_acq y(ci)];
    % poly fit
    p = polyfit(x_acq,y_acq,6);
    yf = polyval(p,x_acq);
    % update the plot
    pause(0.05)
    set(p1, 'XData', x_acq, 'YData', yf );
     
end
hold off

[Dorothee Boegler]

Thank you! I will adopt the animated plot simulating data acquisition method. This is much more elegant than my previous code.

[Mathieu NOE]

Glad it helped !